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Not-so-solid massive core wings: Lightening the core foam

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ragflyer

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Does anyone have an analytical method and coefficients for curved plates under pressure so that we might validate Stanislavz's FEA work?

Billski
Is it not just a pressure vessel between the ribs? So basically hoops stress. The tangential hoop stress would be q*r/t where q is pressure and r is radius of curvature and t is thickness. The radial displacement would be 0.85*qr/(Et) .... assuming mu = 0.3. Am i missing something?
 

stanislavz

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Build a true wing section slice with a (dummy, pine) spar bolted to the table and we could even see how loads which are passed the whole distance of the wing chord affect skin deflections (together with our "inflation load")
Ok. I was teached to take non-standart approaches, because it is fun.. So - if you want to have chord-vise shaped load, cut wing section, but place you sides futher apart at the front, and lesser at the back. And it will have different load of skin at the front, and different, smaller at the back..
 

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wsimpso1

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Billski, Just to verify are you using -alpha *q*b^4/(E*t^3) from Roark, where alpha is 0.0138 if a/b = 1?
Sorry missed this...

Proportions I stated were 12" by 48", and then went narrower. With aspect ratio of 2 giving beta and alpha values close to those for infinity, I simplified the run by using those.

Yes, I started with that equation, which is standard plate theory. It works fine for solid laminate. For composite sandwich like Triax/foam/Biax or the Triax/foam, you have to calculate the equivalent of Et^3 for the laminate. The stress equation also requires an equivalent of t^2.

Billski
 
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wsimpso1

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Caveman with unhelpful response wants to know: " Is it an "analytical method" if someone makes a 36" x 6" sheet of CF to approx the right curvature, bonds it to pine " ribs" cut with a band saw, turns it upside down and dumps sand or gravel inside until the desired loading is reached?" Measure deflection. It could even be varied as desired between nose and tail. In pea gravel (0.0644 lb/cu inch density), the pile inside would need to be about 16" high to equal 1psi.. Sand is easier to get (and get rid of), but is .059 lbs/cu inch, so would need to be piled slightly higher.

It is easier (for me, or probably anyone who has carried buckets of sand around) to appreciate the magnitude of that 1psi load when visualized in this way. The bonding of the skin to any foam ribs, and the tensile strength of the foam rib itself, would seem to be pretty important. Flanges and tapes could be needed, so more weight.
I think I would call this an experimental method. You could also use water. Tilting the arrangement could ramp the pressure. Caveman? Sounds smart to me. Have fun.

Billski
 

wsimpso1

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I'm struggling with the details of that vacuum chamber. 1 psi isn't much, but I'm envisioning a mess of manometers, leaks at hard-to-seal junctions, etc. And if we want to have different pressures at different parts of the airfoil, things get even more complicated.
But if my airfoil is 4 inches wide and I want 1psi of "pull", I can get it with an 8 lb weight pulling on a 2" (chordwise) x 4" spanwise (width of sample) piece of skin. 1 gallon water jug, nylon cord, attach to a bit of something stiff that is roughly the shape of the airfoil underneath. Spray adhesive to stick 1" thick upholstery foam to the wing surface, stick the top of the upholstery foam to the stiff panel tied to the weight. The upholstery foam is only there to spread the load more smoothly over the wing skin, prevent unrealistic locally high loading on a few wing skin spots. Hang the weight over the smoothly rounded edge of the table (PVC pipe as edging?)
36 chordwise linear inches of wing surface = 18 hanging water jugs. Too much clutter? Wet sand has double the density, so use 1/2 gal jugs or half as many 1 gal jugs. Also, it will be less if if some areas are tested at lower loads (for most of our designs, it will be hard to get 1psi aft of the quarter chord point. Maybe a flap at 90 degrees and 180 mph could show positive pressures approaching that.)

Build a true wing section slice with a (dummy, pine) spar bolted to the table and we could even see how loads which are passed the whole distance of the wing chord affect skin deflections (together with our "inflation load") . And, then flaps...
Lots of fun. I'll start saving milk jugs.
I think that the pea gravel or sand sounds like a much more appropriate approach as it is more likely to maintain the pressure across the plates than foam rubber is... with these questions and thought experiments, we begin to see the difficulty in doing a complete simulation for test.
 

wsimpso1

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Is it not just a pressure vessel between the ribs? So basically hoops stress. The tangential hoop stress would be q*r/t where q is pressure and r is radius of curvature and t is thickness. The radial displacement would be 0.85*qr/(Et) .... assuming mu = 0.3. Am i missing something?
Yes, this is a higher stress situation than a simple cylindrical pressure vessel.

The cylindrical part of a thin walled cylindrical pressure vessel changes diameter but not length when pressure difference changes. And the pressure on each side of the vessel wall is assumed the same everywhere. So the radius of the vessel changes when you change deltaP, but there are no moments added to the shell by doing so. This leaves the skin in essentially plain strain. To further talk about it, the hoop stress is twice the stress in the axial direction, while stress in the radial direction is only the pressure in the vessel. This radial stress is generally much lower than the hoop or axial stress, and is frequently ignored.

Go to a wing with a constant pressure on one side and a varying pressure on the other, and the radius and change of radius is varying with pressure, which adds moments to the skin...

There the edge of each panel constrains the panel. We usually assume fixed position and rotation where the skin passes over a rib or spar. This does not require big stiffness in the rib or spar, only that the skin is over one open space, crosses over a rib (riveted or bonded to it) and than is over another open space. The bending on each side of the rib is mostly balanced by the bending on the other side of the rib. This is significant bending moments in the skin and is superimposed over the in-plain stresses.

I am looking forward to the FEA of this case.

So, a good FEA is probably the best way to get at the actual stress case in skins. You can model the wing, impose bending and torsion and pressure distributions and see what the total stress case is for the skins. In a Part 103 UL, inflation is probably insignificant. Get to a transonic or faster airplane and inflation can dominate the stress case for the wing skins and even the fuselage skins. If we go trying to go really flimsy on the wing skins, using a composite shell and some foam, well, this whole topic becomes worth looking at. Better before build than in the aftermath of having to bail out of the test article.

Billski
 
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ragflyer

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Yes, this is a higher stress situation than a simple cylindrical pressure vessel.

The cylindrical part of a thin walled cylindrical pressure vessel changes diameter but not length when pressure difference changes. And the pressure on each side of the vessel wall is assumed the same everywhere. So the radius of the vessel changes when you change deltaP, but there are no moments added to the shell by doing so. This leaves the skin in essentially plain strain. To further talk about it, the hoop stress is twice the stress in the axial direction, while stress in the radial direction is only the pressure in the vessel. This radial stress is generally much lower than the hoop or axial stress, and is frequently ignored.

Go to a wing with a constant pressure on one side and a varying pressure on the other, and the radius and change of radius is varying with pressure, which adds moments to the skin...

There the edge of each panel constrains the panel. We usually assume fixed position and rotation where the skin passes over a rib or spar. This does not require big stiffness in the rib or spar, only that the skin is over one open space, crosses over a rib (riveted or bonded to it) and than is over another open space. The bending on each side of the rib is mostly balanced by the bending on the other side of the rib. This is significant bending moments in the skin and is superimposed over the in-plain stresses.

I am looking forward to the FEA of this case.

So, a good FEA is probably the best way to get at the actual stress case in skins. You can model the wing, impose bending and torsion and pressure distributions and see what the total stress case is for the skins. In a Part 103 UL, this is probably insignificant. Get to a transonic or faster airplane and it can dominate the stress case for the wing skins. If we go trying to go really flimsy on the wing skins, using a composite shell and some foam, well, this whole topic becomes worth looking at. Better before build than in the aftermath of having to bail out of the test article.

Billski
Thanks Billski. I thought you where looking for an analytical solution for just the pressure difference and membrane stresses like the Roarks formula you posted on flat panels. That formula only took the pressure differences into account. Obviously the actual stresses are far more complicated. In general torsion, bending stresses and handling stresses will dominate in most homebuilt designs. As you say though if folks get skimpy on skin in composites membrane stresses may be an issue, though I still think the other cases will dominate. In traditional metal wings as the skins are allowed to buckle at very low stresses there is very little risk of damage to skin as most stresses are taken in tension field (though rib loads due to semi-tension fields is another matter)
 

stanislavz

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Plate, 405mm arc length, radius 770mm or 16.2" / 30.8"

600mm/24" section, deflection 0.02", RF 8.9 :

1607354306914.png

With 9mm foam, Deflection 0.012" RF >10 :

1607354407828.png

Only one ply of 18 oz biax GF, 0.054", reserve 4.3
1607354533317.png

Same as last one, laminas 45/-45, slightly more deflection, but RF is ~ 6

1607354639378.png

And back to cf 450gsm 0/90 , 0.023", Rf > 10:

1607354772115.png

Two plies of 2x300 gsm 0/90 / ~ 22 oz ? 0.0156" and RF is even more

1607354934590.png

CF 2x450 gsm, 0.01" deflection, Rf > 10

1607355200824.png

2x300 gsm cf + 5mm foam

1607355323251.png

And last one for today 450gsm cf, laminas at 45/-45:

1607355061869.png

So on air loads - no problem here... Or milion ribs . On shear due to torsional loads picture is not as happy :) I do not need it now. But may run numbers for others.

Radiused sample was for ga30-4135 airfoil nose section approximation. 1.35 m. / 54" chord. Ok for strutted wing, too thin for cantilever.

Billski will you be able to provide shear loads due to wing torsional loads ? I can build few sections and load them too.
 

Vigilant1

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I suppose M. Colomban chose that thick (19% IIRC) airfoil for the Cri-Cri so he could get a reasonably deep spar for his relatively high AR wing. But he probably also liked that extra panel curvature and the panel stiffness he got from it. Otherwise, maybe the ribs would have been even closer!
 

stanislavz

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I suppose M. Colomban chose that thick (19% IIRC) airfoil for the Cri-Cri so he could get a reasonably deep spar for his relatively high AR wing. But he probably also liked that extra panel curvature and the panel stiffness he got from it. Otherwise, maybe the ribs would have been even closer!
This model was viable only for no-torsionally loaded wing with V struts. You will see different results, then we will add some shear..

FEA is fun and easy, but if some will read my posts and take decision on some images - i would not like this.. So again - Only air loads due to CL to be transfered from skin to ribs/ spar. No torsional loads applied
 

ragflyer

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Torsional loads in the units I prefer is given by max Torque at root = cm*S*V^2*C/391

cm = airfoil pitching moment. It will depend on airfoil section, flaps deployed etc. Assume 0.1 as a reasonable value to start.

S= wing semi span area (half total area) in square feet

V = speed in mph (assume Vd)

C = chord in feet

torque is in ft/lb
 

wsimpso1

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So on air loads - no problem here... Or milion ribs . On shear due to torsional loads picture is not as happy :) I do not need it now. But may run numbers for others.
Well, that is a relief. In a slow airplane a fiberglass skin with no foam is not necessarily a limiting factor. I know in my 268 knot Vd it certainly is.

Billski will you be able to provide shear loads due to wing torsional loads ? I can build few sections and load them too.
Not so simple as you might think. I could do just about any airfoil, but it is a lot of data entry (a failure prone process for this for this slightly dyslexic engineer) and other fuss for me who would rather be out making wingtip lenses. Tell you what, I have the Riblett 37A315 documented, which should be similar to other wings, but not identical.

tau = T*r/J

M = q*Cm*c*S

at 120 knots, q is 49 lb/ft^2, Cm tends to run around -0.05, c we have been talking about is 4ft, and S is 120ft^2. Since we are looking for the pitching moment of one wing at the root, we divide by two. Since we have a real wing with lift falling off towards the tip we multiply by Pi/4. 463 ft-lb, which is also 5552 in-lb.

Let's remember that we also usually have a somewhat lower g limit and max airspeed for flaps deployed. Yeah, lower q, but Cm can go to -1.0, so that case is worht running too.

Radius for tau calc varies widely and is based at the centroid of twist for the foil with the spar in it. My calcs all run wings that end at about .75c because my wings have flaps and ailerons filling the trailing edge, so my skin centroid is about where the main spar is, at .38c, and about 0.02c above the chord line. Since pressures and panel stresses are biggest up hear the leading edge, let's get r for upper skin at 0.15c. works out to 0.236*c = 11.35 inches.

J is kind of neat, I have curve fit it as 0.0886*c^3*t = 17.6 in^4 for a 0.018 (one ply 18 oz BIAX). Plug it into the equation and

tau = 3580 psi . Hmm or about 64.4 lb per linear each skin for a 0.018" skin.

Which has to be superimposed upon the inflation stresses and the bending stresses. We still do not have bending stresses, so let's do them.

Time for another estimator - The bending strain of the wing spar caps at max g pretty much follows the bending strain of the main spar because it is bonded to it. The skin then sees somewhere between 1/4 and 1/3 of the failure strain of the spar cap materials. Why so small? FOS is 2.0, so we get to half right away. Then when we make make strength under bending and shear at something approaching min weight, we end up beefing the caps substantially. Let's call it 1/3 of failure strain. Oh, we are watching the skin at about 0.15c, which puts the skins about 3/4 of the height of the caps. So, let's make it 1/3*3/4 = 1/4 of first fiber failure in the caps.

How much is that in the way of loads? Well, if you can impose strains in certain axes, that is the most straight forward solver. Hmm, E-glass at +/-45 has E of about 1.8Mpsi, T300 at +/-45 is about 8.4Mpsi, strain times thickness times E is load. Unidirectional E-glass first fiber failure strain is about 70kpsi and E is about 4.4Mpsi, so failure strain is 1.6%, and the wing skins will see tensile or compressive strains of about 0.4% strain or about 130 pounds per linear inch in 0.018" thick BIAX. Unidirectional T300 modulus is 181GPa and strengths are 1500MPa, so first fiber strain at failure is about 0.8%, so the wing is seeing about 0.2% strain or about 420 pounds per linear inch in 0.008" thick cloth laminate. Work with other materials and orientation, and you can now figure out what is going on for the models.

So now we have a way to look at inflation, torsion, and bending. So let's look at the total stress state. Top skin in E-glass x, y and shear stresses:
  • X direction has about 1/4 of strength or 18,500 psi compressive plus whatever the inflation stresses are;
  • Y direction has the inflation stresses;
  • Shear along the edges are about 3580 psi.
Each of these produces strains and is run against failure criteria. Or you decide on laminate thickness and put in loads on the edges of the panel and airload on the skin and let the FEA run.

Billski
 

wsimpso1

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Oh, one other thing is that someone has to check if our plate goes into buckling/wrinkling/crippling. If our plate does not go into elastic instability, the FEA is probably pretty good straight up.

If the plate goes into elastic instability, max load in compression can become much smaller, while deflections and how loads are reacted can change significantly. Buckling requires other calculations in closed form analysis and additional tools in FEA. The rules on loads the panel can carry and deflections incurred once it goes into elastic instability change rather dramatically there.

I have not done it before, and am too busy to learn it right now. In FEA, there is a learning curve on elastic stability, buckling, and loads too. Now maybe we are blessed with someone who knows what they are doing on that topic...

Billski
 

stanislavz

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Oh, one other thing is that someone has to check if our plate goes into buckling/wrinkling/crippling. If our plate does not go into elastic instability, the FEA is probably pretty good straight up.
It is first bigger criteria as per my simulations.. I do find rule of skin to shear-web 1/70 ratio, which is minimum if we want to have any buckling stability. Any bigger and can take much less load..

Ok, so i will try to take torque provided by Ragflyer + CL of 1 on ailerons flaps.. When will try to dig on flutter vs wing torsional rigidity. Did see some simple formulas in older books.
 

stanislavz

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Torsional loads in the units I prefer is given by max Torque at root = cm*S*V^2*C/391

cm = airfoil pitching moment. It will depend on airfoil section, flaps deployed etc. Assume 0.1 as a reasonable value to start.

S= wing semi span area (half total area) in square feet

V = speed in mph (assume Vd)

C = chord in feet

torque is in ft/lb
So we have numbers :

1607428372194.png

But at which point it is applied ? Or shell i apply it to stiffness centroid ? ~ at main spar .

1607428835636.png
 

stanislavz

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Some data at 24" singly ply skin 450 cf, RF is at 1.5, loaded at nose section 1.02psi, rear section 0.4 psi unlikly to occur.. :

1607430609740.png
at 9"

1607430905618.png

6 x overload for torsion :

1607431022332.png

And we are out of RF...

Twice skin + 5 mm foam, still no luck:

1607431148809.png

Two plies, but without foam :

1607431368025.png

No buckling..

At 24", two plies, and we have a lot of buckling..

1607431514510.png

24" + added foam - all is much better..

1607431708835.png

Both shows Rf at 0.35, so skin is limiting factor, not skin support against buckling.

With fiberglass 18 oz + foam +18oz :

1607431879130.png

Minimum buckling.

No foam :

1607431936907.png

And no foam at 9"

1607431976238.png

Still poor situation.


In conclusion - cave men can build short section of wing with two overbuild ribs at the ends, and load to check for any wrinkles. And add more ribs after some tests.

Do we need safety factor of 6 on wing torque load ?
 

wsimpso1

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It is first bigger criteria as per my simulations.. I do find rule of skin to shear-web 1/70 ratio, which is minimum if we want to have any buckling stability. Any bigger and can take much less load...
Hmmm, that is new to me (I keep getting more educated all the time). That 1/70 rule is that for a specific material or is it universal. Seems to me that since buckling is a linear function of EI of the section, material would adjust that. E of +/- 45 E-glass laminate is about 1.8Mpsi, while aluminum is 10Mpsi, and steel 30Mpsi. Steel is 15 times our skin material. Anyway, if we use that rule, our one ply 0.018" thick E-glass BIAX allows about a 1.26" free span...

Billski
 

stanislavz

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That 1/70 rule is that for a specific material or is it universal.
Kind of rule of thumb, found in one of Strojnik books.

One, perhaps the most important rule says : we
will tell you what torsional shearing stress you may apply wh en
using equation 2.8 - UNDER THE CONDITION THAT YOU PROMISE TO PREVENT
BUCKLING - USING PROPER METHODS. The designer immediately says
Sure, of course, I accept . What do I have to do? The answer
STIFFEN YOUR SHEARING "FIELDS" .
In the case of the vertical web in the wing spar one may use aluminum, plywood, fiberglass etc.
plates , as long as the longest distance between two stiffeners
is less than , for example,70 times thickness of the material.
If the distance is more , the designer must use considerably lower
stresses.He is always welcome to use shorter distances between
stiffening elements. The stiffening agents may be of any sort :
ta.rs, angles, channels , light~ening holes, punched and flanged
in a single stroke etc. In the case of a stressed skin we do not
have exactly same possibilities, but the basic idea remains the
same: shearing II fields" must remain small and short. One can use
a sandwich_ considered the most economical means if series production
is planned_ or closely spaced ribs , or closely spaced stringers
along the wing span ( p.110 top ).

2.8:

1607438584590.png

I think i will send you that chapter of book.
 
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